Three horizontal ropes are attached to a boulder and produce the pulls shown in

Question

Three horizontal ropes are attached to a boulder and produce the pulls shown in the figure. (Figure 1) Find the x and y components of the pull A rightarrow . Express your answer as a comma-separated pair of components. Find the x and y components of the pull B rightarrow . Express your answer as a comma-separated pair of components. Find the x and y components of the pull C rightarrow . Express your answer as a comma-separated pair of components. Find the components of the resultant of the three pulls. Express your answer as a comma-separated pair of components. Find the magnitude of the resultant pull. Find direction (the counterclockwise angle with the +x axis) of the resultant pull. Please give your answer in the interval [0, 360] degree .

Explanation / Answer

A)

Here ,

Ax = A*cos(30)

Ax = 100 * cos(30)

Ax = 86.6 N

Ay = A*sin(30)

Ay = 100 * sin(30)

Ay = 50 N

Ax , Ay = (86.6 , 50 ) N

B)

Bx = -80*sin(30)

Bx = -40 N

By = 80 * cos(30)

By = 69.3 N

Bx , By = (-40 , 69.3 ) N

C)

Cx = -40 * cos(53)

Cx = -24 N

Cy = -40 * sin(53)

Cy = -32 N

Cx , Cy = (-24 , -32) N

D)

Fx = 86.6 - 40 - 24

Fx = 22.6 N

Fy = 50 + 69.3 - 32

Fy = 87.3

Fx, Fy = (22.6 , 87.3) N

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